C#. Имеется несколько классов, при вызове одного из классов выдает ошибку, в чем проблема?

Question

System.NullReferenceException: "Object reference not set to an instance of an object."

Contact_Book.book.Letters.get[] было null.

namespace Contact_Book
{
    public class Person
    {
        private string surname;
        private string number;
        public string Surname
        {
            get { return surname; }
            set { surname = value; }
        }
        public string Number
        {
            get { return number; }
            set { number = value; }
        }
    public Person(string surname, string number)
    {
        Surname = surname; Number = number;
    }
}

public class Letter
{
    private char pageletter;
    private Person[] people;
    public char Pageletter
    {
        get { return pageletter; }
        set { pageletter = value; }
    }
    public Person[] People
    {
        get { return people; }
        set { people = value; }
    }

    public Letter(char pageletter)
    {
        Pageletter = pageletter;
        People = new Person[1];
    }
}
public class book
{
    private Letter[] letters;
    public Letter[] Letters
    {
        get { return letters; }
        set { letters = value; }
    }

    public book()
    {
        Letters = new Letter[3];
    }

    public void Print(string neededname)
    {
        int i = 0;



        char firstletter = Convert.ToChar(neededname.Substring(0, 1));
        while (i < Letters.Length)
        {
            if (Letters[i].Pageletter == firstletter)
            {
                int j = 0;
                while (i < Letters[i].People.Length)
                {
                    if (Letters[i].People[j].Equals(neededname))
                    {
                        Console.WriteLine(neededname + "'s phone number is:");
                        Console.WriteLine(Letters[1].People[j].Number);
                    }
                }
            }

        } 

    }

    static void Main()
    {

        Person p1 = new Person("Ivanov", "+7123456789");
        Person p2 = new Person("Petrov", "+7344235434");
        Person p3 = new Person("Whatever", "+734324324");

        Letter l1 = new Letter('I');
        Letter l2 = new Letter('P');
        Letter l3 = new Letter('W');
        l1.People[0] = p1;
        l2.People[0] = p2;
        l3.People[0] = p3;
        book phonebook = new book();
        phonebook.Print("Ivanov"); 

    }
}    

}